As a writer, I admire the philosophers who tell me that our dreams have infinite scope and breadth and can find unlimited expression in our writings.
As the husband of a librarian, however, I am fascinated by the indisputable mathematical fact that the number of ways in which those ideas - about anything - can be expressed is, in fact, a finite number, based solely upon the number of letters in the alphabet (and other symbols we use in writing).
A century ago, a German writer, Kurd Lasswitz, did the math and wrote a short story called "The Universal Library." It has been a favorite of mine since high school days. While written in German, it was translated into English by the popular science writer, the late Willy Ley.
Lasswitz sets certain rules for the library, the better to quantify things. All capitals, lower case letters, numbers, etc., plus important symbols can be used - say a total of 100 characters, all in a single typeface. The size of each book is set to 500 pages - shorter books would simply be left blank, for a blank space would be one of the characters; longer books would break into multiple volumes. Each page has 40 lines, with fifty characters per line. So each book would have room for 50 times 40 times 500 characters, or a total of one million characters per book.
Still with me? The first volume would be completely blank - that is the "blank" character is repeated 1 million times. The second volume is blank until the last position on the last page, where an "a" appears. In the third volume, the "a" has moved up one place. And so on - the "a" moving up through the one million positions in each successive volume until it reaches the beginning, to be replaced by each of the successive 99 characters. So much for the first 100 million volumes. The next volume would begin with "aa" in the last two positions, and the two-letter combinations would move up through the next 100 million volumes - and so on, until you had every possible combination of every character.
There are, of course, some practical difficulties. While the library must, of necessity, contain a complete and accurate index to itself, it must also contain every false and erroneous index. Every truth, great and small, would be offset by every lie; there would, quite obviously, be huge sections of the library that are merely gibberish - or that begin, perhaps, with a sonnet by Shakespeare and then turn into gibberish. Finding the useful books would be challenging, to say the least.
But the point is that the universal library is NOT infinite. It is finite, because it is created by publishing books that contain every conceivable combination of the characters of the alphabet. The total number of volumes needed can be written quite easily, too, as 102,000,000 - or a 1 followed by 2 million zeros. That number is beyond astronomical; it is far too large for us to grasp, let alone name. Lasswitz goes on to calculate the number of universes packed with books that would be needed to hold the library - well you get the idea.
He's not arguing that we don't have the infinite capacity to dream - just that it is possible to determine exactly how many books would be needed to contain every idea we can possibly communicate. That number is finite - unimaginably large, impossible ever to do, but finite.
If interested, you can find this story in Clifton Fadiman's marvelous anthology of fantasy and science fiction based on mathematical themes, "Fantasia Mathematica," which has been one of my favorites for half a century. I highly recommend it.